Flexure hinge

ABSTRACT

A flexure hinge with two material segments connected to each other via a material tapering to a thin spot which defines a pivot axis between the two material segments. The material segments are provided with recesses such that the strength existing in the thin spot with respect to normal stresses or bending stresses is kept largely constant within a distance from the thin spot.

TECHNICAL FIELD OF THE INVENTION

The invention concerns a flexure, or thin spot, hinge for movableconnection of material segments.

BACKGROUND OF THE INVENTION

Hinges are often used in industry to connect components movably to eachother. The hinges are intended to allow movements and transfers of forcein certain directions, but prevent them in other directions. An exampleof this is a solid body or flexure hinge. In this case two materialsegments that are connected to each other monolithically are providedwith a material tapering (a so-called “thin spot”) in order to enablemovements about a pivot axis formed by the thin spot. Pivoting movementsabout axes perpendicular thereto and translatory relative movements ofthe two material segments, however, are prevented.

Such flexure hinges are known in particular from modern weighingtechnology, which utilizes monolithic link arm mechanisms, so-calledmonoblocks. Through this, production costs are reduced and theprecision, reproducibility, and long term stability are improved at thesame time. In the case of the monoblocks for balances, thin spots areused, among other places, as hinges for parallelogram arms, for levers,and on coupling rods. In the case of balances that operate on theprinciple of electromagnetic force compensation, the deflections of thelevers or parallel arms are as a rule very small, so that only smallpivot angles arise at the hinges.

Processes known for production of thin spots on monoblocks includechip-cutting processes, but erosion (wire erosion) and laser beammachining are also known techniques.

A thin spot has the task of reliably transferring tensile andcompressive forces in the form of normal stresses. On the other hand,the thin spot is intended to produce as low as possible a resistance topivoting about its pivot axis and the bending stiffness about the pivotaxis should therefore be as low as possible. This is why the desire isto remove as much material as possible in the region of the thin spot(reduction of the bending stiffness), while maintaining a minimumstrength, in particular for normal stresses. To achieve this, thesolutions known from the prior art either seek to reduce the crosssection of the thin spot further, where the reduction is kept constantover the entire width of the block, or the width of the thin spot isreduced further by, for example, recesses disposed centrally on thepivot axis of the thin spot. Through-holes or drillings as shown inJP2004340593 A1 and U.S. Pat. No. 7,307,226 B2, or troughs ordepressions as shown in DE 10 2013 108 097 B4 or DE 100 15 311 B4 areknown. In any case, besides the desired reduction of the stiffness, thestability (load capacity, strength) is always undesirably reduced, evenif it is represented as “acceptable” in the literature.

It is disadvantageous with these known solutions that with a decrease ofthe bending stiffness, the strength with respect to normal stressesbecomes reduced, and vice versa. Moreover, due to material removal, inparticular in the thin spot, regions with increased or decreasedmaterial stress (hot spots) always result.

SUMMARY OF THE INVENTION

The present invention is directed to flexure hinges that are improvedthrough material removal to preferably reduce the bending stiffness ofthe hinge while maintaining the strength of the thin spot. Aspects ofthe invention encompass flexure hinge structures, measurement apparatusincluding flexure hinge structures, and methods of producing flexurehinges.

The invention is based on the recognition that the strength propertiesprevailing at the thin spot that involve normal stresses and bendingstresses can also be affected in regions at a distance from the thinspot by means of specially shaped recesses. These recesses arepositioned and shaped so that the strength of a cross section thatpasses through the recesses and is at a distance from the thin spotcorresponds to that which a comparable cross section through the thinspot itself has. “Strength” in this case can refer to the strength withrespect to normal stresses, in particular in the lengthwise direction Yof the hinge, or to the strength with respect to bending about the pivotaxis (WD) of the hinge.

The principle according to the invention of maintaining the strengthconstant over a selectable length on both sides of the thin spot is tobe understood to mean that certain, in particular production related,tolerances cannot be excluded or even predetermined. Because of thecomplex shaping of thin spots and the recesses penetrating them,mutually corresponding strengths are understood, among other things, tobe ones that have the goal of a strength property that coincides as muchas possible, since in practical terms the goal of an absolutelyidentical strength at different imaginary cross sections can be achievedonly with difficulty or not at all.

It is achieved through the design of the recesses of a flexure hingeaccording to the invention that the strength existing in the thin spotalso remains largely unchanged over a distance from the thin spot, eventhough the material thicknesses increases beyond the thin spot.

The thin spot itself, as the thinnest spot of the hinge, preferablyremains as a “neutral zone,” which is designed as intact material.Weaknesses of the thin spot due to recesses made in the thin spot itselfcan advantageously be omitted.

A flexure hinge according to one aspect of the invention comprises afirst and a second material segment, which are monolithically joined toeach other via a thin spot. The material thickness of the two materialsegments measured in a thickness direction X tapers along a taperingzone in the direction of a lengthwise direction Y perpendicular to the Xdirection up to the thin spot, which has a minimal thickness at thispoint. The pivot axis of the thin spot extends along a width direction Zrunning perpendicular to the X and Y directions.

A cross section QD running through the thin spot in an X-Z plane andhaving a section width running in the Z direction yields a cross sectionarea AD. The cross section area AD can comprise a plurality of partialareas, if the thin spot is divided by openings lying in it and thesection width being considered includes such openings.

The cross section area AD thus formed has a certain strength withrespect to normal stresses in the Y direction, where the strength withrespect to shear stresses in the Z direction and in particular in the Xdirection is of subordinate importance. Furthermore, the cross sectionarea AD lying in the thin spot has a bending strength (moment ofresistance about the pivot axis), which is selected to be as small aspossible by means of a low material thickness of the thin spot in the Xdirection.

The invention is based on the idea of making the strength existing incross section area Ao [identical] with respect to a certain load even inanother cross section (Q′, Q″ . . . ) parallel to cross section area Ao,which is taken in a tapering zone parallel to cross section Qo, wherematerial is removed from the hinge by means of recesses.

The cross sections (Q′, Q″ . . . ) are viewed at various positionsperpendicular to the Y direction and along it. They each generate crosssection areas (A′, A″ . . . ) in the hinge, which can be composed ofindividual cross section areas and can be bounded at least partially bythe recesses. According to aspects of the invention, the recesses andthus the partial cross section areas are chosen so that the Z width ofthe partial cross section areas decreases with increasing distance ofthe cross sections (Q′, Q″ . . . ) from the thin spot position (Yo). Theforce-transmitting area of the individual partial cross section areasthus becomes thinner. To maintain the desired strength or stiffness, theindividual partial cross section areas instead become increasinglythicker when the X wall thickness of the tapering zones increases withincreasing Y direction.

The recesses are positioned and designed in the tapering zone or zonesso that the said behavior applies at least along a segment section L_(U)running in the Y direction. Preferably, the number of partial crosssection areas remains constant along the segment L_(U). In addition, thepartial cross section areas preferably have a regular geometric, inparticular rectangular, shape.

The recesses are chosen in shape and position so that the strengthexisting in the thin spot also does not or only negligibly changes alongan increasing Y distance from the thin spot. This property is achievedbecause a cross section area Q′, Q″ . . . produced by the at least onerecess produces, along a section plane X-Z with the section width B, across section A′, A″ . . . (which can be made up of a plurality ofpartial areas), the strength property of which largely corresponds tothat of the cross section area AD determined in the thin spot itself.

If the material thickness increases steadily in the Y direction startingfrom the thin spot, the constant strength with increasing Y distancefrom the thin spot will be achieved in that the cross section Q′ hasgeometric shapes, in particular rectangles, whose width measured in theZ direction decreases with increasing Y distance from the thin spot.This takes into account the circumstance that the material thickness ofthe tapering zones increases with increasing Y distance from the thinspot (for example quadratically). Correspondingly, the Z width of thecross section area A′, A″ . . . or its partial surfaces must becomesmaller with increasing Y distance from the thin spot, in order toachieve overall the same strength as at the thin spot itself.Preferably, the cross section area A′, A″ . . . formed in each caseremains constant along a segment section (LU) running in the Ydirection, and it especially preferably corresponds to the cross sectionarea AD in the thin spot.

If constant normal stresses (in the Y direction) are desired, therecesses are designed so that the cross section area A′ in cross sectionQ′ largely corresponds to cross section area AD in the thin spot crosssection QD (area equivalent). In the lengthwise direction Y of thehinge, the cross section area transferring the normal stresses remainsconstant over a certain segment LU, so that the following applies

σ=F/A=const.

In a manner different from leaf springs, which do have a constantthickness, but have an undefined point of rotation, the point ofrotation in the case of the embodiment aimed at the area equivalentcontinues to be defined at the site of the least thickness or the leastmoment of resistance. As a result, in this variation the responsivenessof a balance could be increased by 20% through the reduction of thebending stiffness, while keeping the hinge thickness and strength thesame.

If, as an alternative to the area equivalent, the bending stiffness isto be reduced without reducing the bending strength, then the moment ofresistance (moment of resistance equivalent) must be kept constant withincreasing Y distance from the thin spot, so that the moment ofresistance of the cross section area AD about the pivot axis WD largelycoincides with the relevant moments of resistance of the cross sectionarea A′, A″ . . . in cross section Q′, Q″ . . . .

The thin spot is often generated by two borings in a material block, sothat it remains as a bridge between the lateral surfaces of two roundcylinders lying next to each other. The cross section QD at the thinspot, when the thin spot is formed along the imaginary section width Bfrom intact material continuously without openings, then has the shapeof a rectangle. The cross section area AD results in this case from thesection width B multiplied by the remaining thickness XD of the thinspot. If the thin spot is to be penetrated by one or more openings alongthe imaginary section width B, there will result a plurality ofindividual rectangular cross section areas lying side by side in the Zdirection, which add up to the total surface AD.

According to another advantageous embodiment of the invention, the atleast one recess in a tapering zone is chosen so that the cross sectionQ′, Q″ . . . generates a plurality of geometric shapes, preferably ofthe same size, where these are preferably rectangles. In each case,according to the design of the walls of the recesses, the individualpartial cross sections can, however, also have the shape of a trapezoid,a parallelogram, a polygon, or a surface formed from straight linesand/or curves. In an especially preferred case the recesses have wallsurfaces that run parallel to the X direction, so that individualrectangles arise in the cross section Q′, Q″ . . . .

The recesses in accordance with the invention do not have to completelypenetrate the tapering zones. The term “recesses” is also intended toinclude depressions. For example, it is conceivable to introducedepressions lying opposite each other in the X direction and offset fromeach other in the Z direction in one or both tapering zones. In the sameway, recesses that completely penetrate the tapering zone can becombined with depressions that do not. What is decisive for the resultin accordance with the invention is the design of the recesses so thatthe strength of the thin spot corresponds roughly with that in theregion of the recesses.

An advantageous embodiment of the invention provides that at least onerecess in a section with a Y-Z plane has an outline in which twoboundary lines extend out from a common vertex, which lies closest tothe thin spot, in the Y direction from the thin spot, where at leastone, preferably both boundary lines move away, preferably symmetrically,from an X-Y plane passing through the vertex, with increasing Ydistance. As is evident from the drawings described below, the course ofthe boundary lines takes into account the increasing material thicknessof the tapering zone with increasing Y distance from the thin spot, sothat the cross section area A′, A″ . . . resulting from the section Q′,Q″ . . . has essentially the same strength for each section through therecess as the thin spot itself. Thus, according to the invention, thecurve is a function of the material thickness, which is dependent on theY position. In the case of a steadily increasing material thickness inthe tapering zone, a monotonic dependence of the course of the curve ofthe boundary line on the Y distance from the thin spot results. Theresult according to the invention is, however, also achieved when thematerial thickness does not steadily increase, provided this is takeninto account in the shape of the recesses to achieve cross section areaswith largely constant strength.

Preferably, the flexure hinge is provided with a plurality of recesses,which lie side by side in width direction Z. This results in a uniformstress distribution over the viewed section width B. Expediently, therecesses have the same shape, which simplifies production andcalculation. Moreover, the recesses preferably have the same spacingsfrom each other in the Z direction, which distributes stresses stillmore uniformly over the width of the hinge.

One embodiment of the invention provides that all recesses are spaced alittle in the Y direction from the thin spot, preferably between 0.025and 0.05 millimeters. Through this, the thin spot obtains a certain Y“length,” which contributes to the stability of the hinge in thisregion.

Preferably, recesses are provided on both sides of the thin spot in theY direction, thus in the first and opposing second tapering zones. Thisresults in a largely symmetric stress curve on both sides of the thinspot. In order to avoid stress peaks (hot spots), the recesses of thetwo tapering zones can be disposed offset from each other in the Zdirection. A plurality of recesses can be disposed side by side inidentical or different shape in the Z or Y direction.

The recesses do not have to be completely surrounded by material of thetapering zone. An embodiment in which at least one recess is formed as apocket introduced laterally in the Z direction into the edge of thetapering zone is also conceivable. Preferably, a plurality of suchpockets is provided symmetrically to an X-Y plane, which divides thehinge centrally in the Z direction.

According to an advantageous embodiment, the thin spot is divided into aplurality, preferably, two, thin spot segments Da, Db lying side by sidein the width direction Z by at least one opening. A single centralopening H in the thin spot, which can also penetrate the tapering zones,reduces the thin spot to two connecting regions spaced apart from eachother in the Z direction. The opening removes material where it makesonly a small contribution to the transfer of moments about a Y axis or Xaxis lying centrally in the hinge, which is different than in the edgeregions, which have a greater distance to the center in the direction ofthe Z axis.

Preferably a plurality of recesses are disposed in the tapering zone orzones away from the thin spot. They can be spaced regularly orirregularly with respect to each other in the Y or Z direction, and canlie individually or in groups in the same or offset Z position withrespect to the pivot axis. Alternatively or in addition, recesses can beprovided on both sides of the pivot axis having the same or differentdistances to the pivot axis. Preferably, recesses are provided in atapering zone in the Z direction that lie one behind the other withconstant Z distance from each other and constant Y distance from thepivot axis, while a like arrangement of recesses is provided in theother tapering zone, thus on the other side of the pivot axis, whereboth recess groups are offset from each other in the Z direction by halfthe Z distance of the individual recesses. Preferably, one or allrecesses have the same Y-Z cross section.

The production of recesses is preferably to take place by means of alaser beam (in this regard see Application DE102016105985).

The machining of the hinge to produce the recesses preferably takesplace on both sides of the thin spot (looking in the X direction), sothat, for example, the beveling of the machined edge that occurs inone-sided laser machining (conical shape through laser beam machining),and thus the undesirable characteristic torque that arises, is avoidedor reduced.

The invention is suitable for all kinds of hinges, especially formonolithic solid body hinges and/or inserts in micromechanics. Itconcerns preferably measurement equipment, in particular balances with aflexure hinge according to the invention. Said hinge preferably forms apart of a lever, a coupling rod, a rotary hinge, a free flex pivothinge, or a parallel arm mechanism. Balances can in particular operateby the principle of electromagnetic force compensation, strain gauge(DMS), or vibrating string.

These and other advantages and features of the invention will beapparent from the following description of representative embodiments,considered along with the accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 shows a perspective view of a flexure hinge according to theinvention.

FIG. 2 shows a first perspective section of the hinge shown in FIG. 1.

FIG. 3 shows a second perspective section of the hinge shown in FIG. 1at a section plane further from the thin spot of the hinge as comparedto the section of FIG. 2.

FIG. 4 shows a third perspective section of the hinge shown in FIG. 1 ata section plane further from the thin spot of the hinge as compared tothe section of FIG. 3.

FIG. 5 shows a schematic top view of a section of a flexure hinge.

FIG. 6 shows a perspective view of a flexure hinge segment.

DESCRIPTION OF REPRESENTATIVE EMBODIMENTS

FIG. 1 shows a flexure hinge according to the invention in a simplifiedperspective view. The hinge comprises two material segments M1, M2,which are monolithically joined to each other via a thin spot D. Thethin spot D is formed by two tapering sections V1, V2, which extend in alengthwise direction Y toward each other as part of the materialsegments M1, M2, where the thickness measured perpendicular thereto inthe X direction steadily decreases up to a minimal thickness XD, atwhich the actual thin spot D exists. It extends along a pivot axis WD ina width direction Z, which is perpendicular to the X and Y directions.The first material segment M1 can be pivoted with respect to the secondmaterial segment M2 about the thin spot D, where an idealized pivot axisWD runs in the Z direction at the lengthwise position YD of the thinspot D. An opening H made centrally in the thin spot D divides the thinspot into two segments Da and Db in the Z direction.

A plurality of recesses U1, U2 of which not all are provided withreference numbers in the figures for reasons of clarity, penetrate thefirst and second tapering zones V1, V2 on both sides of the thin spot D(in the Y direction). The recesses U1, U2 are chosen so that thestrength properties of the hinge at the thin spot D approximatelycoincide with the strength properties of the hinge at a distance fromthe thin spot that extends to the recesses U1, U2. The following figuresexplain this characteristic provided by recesses U1, U2 in more detail.

FIG. 2 shows a section of the thin spot D with the width B (in the Zdirection), in a magnified and sectioned view. A section plane ED, whichpasses through the thin spot in the X-Z direction, produces a section QDwith cross section area AD. The resulting cross section area AD hascertain strength properties with respect to the normal stresses in the Ydirection or with respect to bending moments about the pivot axis WD.Since the thin spot D is formed along the imaginary section with Bwithout interruptions, this results in a single cross section area AD,which has a rectangular shape because of the cylinder section shapedsurface of the tapering zones V1, V2.

FIG. 3 shows a sectional view comparable to FIG. 2, where in this case asection plane E′ shifted parallel to section plane ED in the Y directionpasses through the region of the tapering zone V1, which is penetratedby the recesses U1. Correspondingly, a number of individual rectangularcross section areas lying side by side in the Z direction, which add upto a total area A′, result from the section Q′ of the plane E′ with thetapering zone V1. The individual rectangular areas (up to the segmentslying at the edge in the Z direction) have a width R′z. According to theinvention the recesses U1 are chosen so that the resulting cross sectionarea A′ coincides with the cross section area AD (area equivalent)formed in the thin spot. From this it follows that a tensile orcompressive force in the thin spot D applied to the hinge in the Ydirection generates the same stress (σ=F/A) as in the region of theplane E′ or the cross section Q′ that is there.

FIG. 4 shows another cross section Q″, which results from theintersection of an additional section plane E″ parallel to the planes EDand E′, with the tapering zone V1, at a Y position that is still fartherfrom the thin spot than the section plane E′, but still within thesegment LU. The resulting cross section area A″ is further composed ofindividual rectangles, the width R″z of which (possibly with theexception of the section lying at the edge in the Z direction) is,however, smaller than in the case of cross section Q′. However, becausethe material thickness of the tapering zone V1 increases with increasingY distance from the thin spot, the thicknesses R′x, R″x of theindividual partial cross section correspondingly increase. As a result,it follows from the shape, chosen per the invention, of the recesses U1along the segment LU that the cross section area A″ also correspondswith the cross section area A′ or AD (area equivalent). This effect,thus the area stress or area load that largely remains constant withincreasing Y distance from the thin spot D, applies in the embodimentshown along the selected segment LU because of the suitable shape of therecesses U1. The segment LU can extend over the entire Y length of arecess U1, U2 or can involve only a part of it.

An imaginary shift of the section plane E along the segment LU in thisembodiment example always produces a total cross section A′, A″ . . . ,the size of which corresponds with that of AD of the thin spot D.

The flexure hinge represented in FIGS. 2 to 4 was created by means ofits recesses U1, U2 so that the sections QD, Q′, and Q″ formed along thesegment LU always produce the same total cross section area, so thattensile or compressive stresses along the segment LU and in this respectindependent of the Y distance to the thin spot D remain largelyconstant.

The same principle, which is not shown in the figures, also applies if,instead of the normal stresses, the bending stresses, which result froma bending of the material segments M1, M2 relative to each other aboutthe Z axis (moment of resistance equivalent), are to be kept constant.Since the moment of resistance of a cross section area to bending isoverproportional to the height of the cross section (in this case on thethickness R′x, R″x of the individual partial cross sections), therecesses U1, U2 are chosen correspondingly so that the relevant widthR′z, R″z of the partial cross sections is overproportionally reducedwith increasing Y distance, in order to produce a constant moment ofresistance as a result.

FIG. 5 shows a section of the flexure hinge according to the inventionfrom FIGS. 1 to 4 in a top view in the X direction. The thin spot Dextends in the width direction Z along an idealized pivot axis WD at theY position of the thin spot, YD. In the tapering zones V1, V2 on bothsides of the thin spot D in the Y direction are approximately triangularrecesses U1, U2, as was already described in FIGS. 2 to 4. The outlineof each recess U1, U2 comprises in this case two boundary lines Ga, Gb,which, starting from a common vertex S, extend symmetrically on bothsides of an imaginary section plane ES, which runs in the X-Y directionthrough the vertex S. The recesses U1, U2 are each bounded at their endsturned away from the thin spot D by wall segments running in the Zdirection.

As FIG. 5 also shows, the recesses U1, U2 do not border directly on theidealized pivot axis WD of the thin spot D, but rather have a small Ydistance from it. To avoid hot spots and undefined weaknesses of thethin spot, the recesses U1, U2 first begin at a small Y distance fromthe thin spot D.

FIG. 6 shows a perspective of a flexure hinge according to the inventionwith the recesses U1, U2 in the tapering zones V1, V2.

As used herein, whether in the above description or the followingclaims, the terms “comprising,” “including,” “carrying,” “having,”“containing,” “involving,” and the like are to be understood to beopen-ended, that is, to mean including but not limited to.

Any use of ordinal terms such as “first,” “second,” “third,” etc., inthe following claims to modify a claim element does not by itselfconnote any priority, precedence, or order of one claim element overanother, or the temporal order in which acts of a method are performed.Rather, unless specifically stated otherwise, such ordinal terms areused merely as labels to distinguish one claim element having a certainname from another element having a same name (but for use of the ordinalterm).

In the above descriptions and the following claims, terms such as top,bottom, upper, lower, and the like with reference to a given feature areintended only to identify a given feature and distinguish that featurefrom other features. Unless specifically stated otherwise, such termsare not intended to convey any spatial or temporal relationship for thefeature relative to any other feature.

The term “each” may be used in the following claims for convenience indescribing characteristics or features of multiple elements, and anysuch use of the term “each” is in the inclusive sense unlessspecifically stated otherwise. For example, if a claim defines two ormore elements as “each” having a characteristic or feature, the use ofthe term “each” is not intended to exclude from the claim scope asituation having a third one of the elements which does not have thedefined characteristic or feature.

The above described preferred embodiments are intended to illustrate theprinciples of the invention, but not to limit the scope of theinvention. Various other embodiments and modifications to thesepreferred embodiments may be made by those skilled in the art withoutdeparting from the scope of the present invention. For example, in someinstances, one or more features disclosed in connection with oneembodiment can be used alone or in combination with one or more featuresof one or more other embodiments. More generally, the various featuresdescribed herein may be used in any working combination.

REFERENCE NUMBER LIST

-   -   X Thickness direction    -   Y Length direction    -   Z Width direction    -   M1, M2 Material segment    -   V1, V2 Tapering zone    -   D Thin spot    -   Da, Db Thin spot segments    -   H Opening    -   WD Pivot axis    -   U1, U2 Recesses    -   QD Cross section through thin spot D    -   Q′v, Q″v Cross section through tapering zone    -   ED Section plane through thin spot    -   E′, E″ Section planes through tapering zone    -   ES Section plane through tapering zone    -   B Section width    -   RX Thickness of a partial cross section area    -   RZ Width of a partial cross section area    -   AD Cross section area through the thin spot    -   A′, A″ Cross section area in the sections Q′, Q″    -   LU Segment section in the Y direction.

1-14. (canceled)
 15. A flexure hinge comprising: (a) a first materialsegment and a second material segment monolithically connected togetheralong a thin spot which defines an imaginary pivot axis between thefirst material segment and the second material segment, at least one ofthe first material segment and the second material segment having athickness along a direction X which tapers in a tapering zone along adirection Y perpendicular to the direction X to a minimal thin spotthickness, the imaginary pivot axis extending in a direction Zperpendicular to the direction X and the direction Y; (b) at least onerecess positioned in the tapering zone of the at least one of the firstmaterial segment and the second material segment; and (c) wherein the atleast one recess is formed so that a plane defined by the direction Xand the direction Z passing through the at least one recess intersectsthe respective material segment to define cross section areas spacedapart along the direction Z and comprising geometric shapes the width ofwhich along the direction Z decrease with increasing distance along thedirection Y from the position of the thin spot along the direction Y.16. The flexure hinge of claim 15 wherein the cross section areasdefined at a given direction X and direction Z plane passing through theat least one recess together provide a strength that corresponds, withintolerances, to the strength provided by the cross section area definedby the intersection of a direction X and direction Z plane passingthrough the thin spot.
 17. The flexure hinge of claim 15 wherein the atleast one recess is formed such that along at least a portion of thelength of the at least one recess along the direction Y, the crosssection areas define a constant total area regardless of the point alongthe direction Y at which the given direction X and direction Z planeintersects the at least one recess.
 18. The flexure hinge of claim 17wherein the constant total area is equal to the area defined by theintersection of the direction X and direction Z plane through the thinspot.
 19. The flexure hinge of claim 15 wherein along at least a portionof the length of the at least one recess along the direction Y, a momentof resistance about the imaginary pivot axis remains constant.
 20. Theflexure hinge of claim 15 wherein the cross section of the thin spotdefined by the intersection of the direction X and direction Z plane atthe thin spot has the shape of one or more rectangles.
 21. The flexurehinge of claim 15 wherein the cross section areas spaced apart along thedirection Z comprise a plurality of identical geometric shapes.
 22. Theflexure hinge of claim 15 wherein the at least one recess has an outlinein a direction Y and direction Z plane in which: (a) two boundary linesextend away from the thin spot along the direction Y from a commonvertex which comprises the part of the at least one recess lying closestto the thin spot; and (b) where one or both boundary lines depart from aplane defined by the direction X and direction Y plane lying at thevertex, the departure being symmetric along a curve with increasingdistance from the thin spot along the direction Y.
 23. The flexure hingeof claim 22 wherein a segment of the curve is formed in dependence onthe material thickness of the tapering zone given at the respectiveposition along the direction Y.
 24. The flexure hinge of claim 15including multiple recesses identical in shape and lying side by sidealong the direction Z.
 25. The flexure hinge of claim 15 wherein one ormore recesses are provided along the direction Y in each of the firstmaterial segment and the second material segment on both sides of thethin spot.
 26. The flexure hinge of claim 25 wherein the first materialsegment and the second material segment each include a respectivetapering zone and at least one recess is provided in each tapering zoneand wherein each recess is positioned in the same distance from the thinspot along the direction Y.
 27. The flexure hinge of claim 15 whereinthat the thin spot is divided by at least one opening into a pluralityof thin spot segments that lie side by side in the direction Z.
 28. Ameasurement apparatus comprising the flexure hinge of claim 15 whereinthe flexure hinge is part of a lever, a coupling rod, a rotating hinge,a free flex pivot hinge, or a parallel arm mechanism.
 29. A method forproducing a flexure hinge according to claim 15 wherein the at least onerecess is introduced into the tapering zone at least in part with alaser applied on both sides of a direction Y and direction Z plane lyingat the imaginary pivot axis.